Long distance multi-day bicycle tours are a highly popular form of exercise and recreation among a fast-growing population of cyclists. Navigation tools that assist multiday bicycle tour planning or generate small-scale bicycle routes are known, but lack the essential services needed to construct customized long distance bicycle tour routes. Further, while network representations of the road and other map features are widely used in mapping applications and route planning, few (if any) are tailored to the needs of bicyclists traveling long distances. Elevation can be added to road network data to calculate slope and produce maps and routing applications for cyclists interested in road gradient, but elevation and grade alone are not sufficient to construct multi-day tours customized to different levels of riding expertise.
Routing applications require the use of graphs to represent road network structure. The traditional representation of a road map uses nodes in the graph to represent road intersections and edges or arcs to represent the sections of road between intersections. Several well-known network flow problems that use graph representations are discussed by Ahuja et al., including the shortest path, maximum flow, minimum cost flow, and multicommodity flow problems. Ahuja, R. K., Magnanti, T. L., and Orlin, J. B. (1993). Network Flows: Theory, Algorithms, and Applications. Prentice Hall, Inc. Graph representations of roads have been used in GIS-based routing for a variety of applications, including modeling water runoff, choosing optimal roads to reach timber stands in forests, and routing the collection of solid waste in India. Extensions and manipulations to the traditional road graph model have also been made in GIS applications in order to capture road topology. Spei{hacek over (c)}ys and Jensen developed a graph representation of a road network that combines a two-dimensional representation of roads with a multi-graph presentation that simultaneously captures the details of road features and allows for routing. Spei{hacek over (c)}ys, L. and Jensen, C. S. (2008). Enabling location-based services-multi-graph representation of transportation networks. Geolnformatica, 12(2):219-253. Wilkie et al. created a lane-centric graph representation of roads to produce large-scale traffic simulations. Wilkie, D., Sewall, J., and Lin, M. C. (2011). Transforming GIS data into functional road models for large-scale traffic simulation. IEEE Transactions on Visualization and Computer Graphics, 16(5).
In order to capture land features accurately, the OpenStreetMap (OSM) dataset uses nodes, ways, and relations to represent points, lines, and polygons on the map. This representation presents a challenge for routing. However, tags within the OSM database indicate road location and type (e.g., ‘oneway=yes’, ‘highway=motorway’) and enable routing within the map.
The International Mountain Bicycling Association (IMBA), The Complete Guide to Climbing (by Bike), and ClimbByBike.com each offer a method of classifying the difficulty of a bicycle path. The rating system used by the IMBA uses percent grade incline to categorize path difficulty and defines five levels of difficulty ranging from the least difficult ‘white circle’ to the extremely difficult ‘double black diamond.’ The easiest level has an average percent grade incline of less than 5% and a maximum grade of 10%, while the hardest level has an average percent grade incline of 15% or more and a maximum percent grade of 20% or greater. This method can be used by cyclists as a general guide for existing bicycle trails. Another system of calculating path difficulty is described by Summerson, in The Complete Guide to Climbing (by Bike) (2007). While this method is more sophisticated than the one defined by the IMBA, it can only be used to calculate the difficulty of climbs, or paths with percent grade incline of 0% or greater. In Summerson's model, the difficulty of a path is the product of the square root of the average grade, the total elevation gain, the altitude adjustment, the surface adjustment, and grade variability. The altitude adjustment increases the difficulty of paths above 2000 feet elevation under the assumption that performance decreases noticeably at that elevation and above. Surface adjustment is found by calculating the percentage of the climb that is non-paved and multiplying that by 0.25, assuming that unpaved surfaces are 25% more difficult to ride on than paved surfaces. Finally, the grade variability adjustment increases the path rating by 0.025 if it has two or more segments where the grade of the segment is larger than the average percent grade of the climb by five or more percentage points. However, Summerson's model cannot be used to calculate the difficulty of the example path shown in FIG. 1, as it has sections of road less than 0% grade in incline.
Yet another method used to calculate the difficulty of a path is given by equation (1) below. This method, shown on ClimbByBike.com, considers similar factors.
                              H                      25            ⁢            L                          +                              H            2                    L                +                  L          1000                +                              T            -            1000                    100                                    (        1        )                                                      962.28                          25              ⁢                              (                26466                )                                              +                                    962.28              2                        26466                    +                      26466            1000                    +                                    1062.28              -              1000                        100                          =        62.08                            (        2        )            
In this model, H represents the total elevation gain, L represents the length of climb, and T represents the elevation at the highest point of the path. The difficulty of the path in FIG. 1 can be calculated using this method as shown in (2). However, it is not clear how the output values of this method scale to paths of higher and lower difficulty, and the formula does not adjust difficulty for different categories of cyclists.
Of the existing methods used to calculate the difficulty of a path, one of the more popular methods is based on the total elevation gain, as climbing is often considered the most challenging aspect of cycling. Consider the path shown in FIG. 1. On this path, cyclists would experience a total elevation gain of 671.22 feet and reach a maximum elevation of 871.22 feet. Using elevation gain alone as a measure, this path would be labeled with a high difficulty rating. However, cyclists riding on this path would also experience two sections during the climb with 0% grade and travel downhill after the climb, which would allow them to recover and mitigate the perceived difficulty of the path. As demonstrated by this path example, elevation gain of a route alone may not be an appropriate evaluation criterion for path difficulty.
While the present disclosure describes many of the systems and methods provided herein with respect to cycling, the concepts are equally applicable, and indeed intended specifically to apply to, other modes of travel which may cause perceived exertion, including but not limited to, hiking, jogging, cross-country skiing, and so on.